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Physics + MathPhysics & Math

Fish Use Physics to Avoid Running into Each Other

Groups of birds and fish may harness fluid dynamics to keep just the right distance from each other. Understanding how could help engineers build better robots.

ByKatherine J. WuNOVA WondersNOVA Wonders

Schools of fish might stay together with the help of physics, with leaders creating wakes for their followers to surf in. Image Credit: iStock, UWPhotog

Shimmering schools of fish provide some of nature’s most captivating displays of synchrony. Swimming in perfect unison, these groups almost appear to move as one giant organism. But with so many individuals in the mix, it’s a wonder that more of them don’t crash into each other or fall out of formation.

According to a study published today in the journal PNAS, animals that move in groups through fluids like air or water might have a hefty dose of physics working in their favor. By surfing in the wake of individuals up ahead, schooling fish and flocking birds can keep pace with their leaders—even without mimicking their every move. Understanding these interactions could help engineers build more energy-efficient underwater vehicles and prove useful for harvesting renewable energy from wind or water.

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While scientists have studied how water moves around schooling fish, with living animals, it’s hard to distinguish the effects of a fish’s own actions from the effects of the fluid around it.

“We don’t know what part of this group movement is due to passive interaction through the environment, and what part is due to active control,” says Eva Kanso, a mechanical engineer at the University of Southern California who was not involved in the study.

To parse out the effects of animals’ behavior and the environment on group movement, a team of applied physicists led by Joel Newbolt at New York University took a mathematical approach. Rather than using live animals, the researchers used two wing-like appendages, or hydrofoils, to simulate two individuals—a leader and a follower—moving through a tank of water. The flapping motions of the hydrofoils were driven by a motor, but each wing swam independently of the other.


A murmuration, or flock, of starlings. Birds that keep within a certain distance of each other might be able to benefit from the wake of the individual in front of them. Image Credit: Airwolfhound, Wikimedia Commons

As expected, when the two flappers swam at the exact same speed, the follower easily kept up with the leader. If it slowed down too much, the follower would eventually get left behind, while flapping too fast risked rear-ending the leader.

But if the follower stayed within a certain pocket of disrupted fluid behind the leader—the leader’s “wake”—it hit a cushy buffer that allowed the two to more easily move in harmony. Within this region, even if the follower lagged a bit, it got tugged back up to speed. And if it quickened its pace, it was nudged backward. As long as the follower kept to this subtle sweet spot, it avoided both separation and collision—a comfortable cycle of sync and swim, if you will.

“If you’re in that region, mistakes can be overcome,” says Megan Leftwich, who studies the hydrodynamics of swimming behavior at George Washington University, but was not involved in the study. “Even if you’re pushed out, it’ll self-correct, and you’ll be pulled back to where you want to be.” This also meant that the follower didn’t have to copy the leader’s every move: As long as it stayed in that zone of safety, the second hydrofoil could follow its own rhythm.

The researchers also observed several cases of followers getting tugged forward by their leaders’ movements. In one scenario, the second hydrofoil was able to triple its speed by just casually coasting in the first hydrofoil’s wake.

“To us, that was really impressive,” says study author Jun Zhang, an applied physicist at New York University. “That means birds or fish can relax. They don’t have to be synchronized dancers, or swimmers in an Olympic game, to form a cohesive group.”

This idea may seem familiar, says Jane Wang, who studies the flight dynamics of insects at Cornell University, but was not involved in the new study. Any cyclist or NASCAR fan has probably heard of the idea of drafting: riding or driving close behind another bike or car to minimize the effects of air resistance (and thus, energy expenditure). The conditions aren’t exactly the same because swimming fish and flying birds are flapping, but these groups of animals seem to be working towards a similar goal.

Though the researchers’ model wasn’t set up to measure energetic output, the logical implication of the results is that these followers would also conserve resources, Zhang says.

“This idea of self-organization... seems to come for free,” says study author Leif Ristroph, an applied mathematician at New York University. “Flows help organize the group.”

Of course, the model does have its caveats. With individual agency completely removed from the system, it’s challenging to draw direct parallels to actual birds or fish, Wang says. But, she says, “there is value in doing these experiments. They single out certain effects. You can say, from a physics points of view, ‘This is what’s happening.’”


Fish, such as these sweepers, can form enormous schools. Studying how fish movements are coordinated and affected by the water around them might inform the design of energy-efficient groups of robots or other technologies. Image Credit: Wikimedia Commons

And that knowledge could be put to good use. For instance, engineers might use it to capture renewable energy from wind and water more efficiently, Newbolt says. Understanding these dynamics could also aid in designing submersible robots to explore the deepest depths of the ocean, for instance, or to deliver supplies to remote regions of the globe.

In scenarios like these, the maintenance of an energy-efficient formation could make or break a mission, Leftwich says. “If you’re deploying [multiple robots] all together, you need to ask, ‘What’s the most efficient formation to put them in?’ Too close or too far, and you’ll lose these benefits.” Exploiting that wake, on the other hand, might be key to achieving complex coordination.

Several robotic developments currently underway utilize two sets of flapping wings, says Amy Gao, a mechanical engineer at Johns Hopkins University’s Applied Physics Laboratory who was not involved in the study. “This study is the first to show that the second set of wings can operate at an entirely different [speed] and still be efficient,” she says. “Basically, the second set can harness the energy lost by the first set of wings. That means you can operate an entire system more efficiently.”

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This material is based upon work supported by the National Science Foundation under Grant No. DRL-1420749. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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